# Program to check if N is a Centered Cubic Number

Given a number N, the task is to check if N is a centered cubic number or not.

A centred cubic number counts the number of points which are formed by a point that is surrounded by concentric cubical layers in 3D with i2 points on the square faces of the i-th layer. The first few Centered cube numbers are 1, 9, 35, 91, 189, 341, 559, 855 …

Examples:

Input: N = 9
Output: Yes
Explanation:
9 is the second Centered cube number

Input: N = 6
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to iterate from one and check whether the ith term is equal to N or not.

1. The Nth term of a centered cubic number is given by .
2. Run a loop starting from 1, to find ith centered cube number.
3. Check if the i-th term is equal to N or not. If it is equal, then return true.
4. If i-th term is greater than N, then return false.

Below is the implementation of the above approach:

## C++

 `// C++ program to check if N  ` `// is a centered cubic number ` `#include ` `using` `namespace` `std; ` ` `  `// Function to check if the number N ` `// is a centered cubic number ` `bool` `isCenteredcube(``int` `N) ` `{ ` `// Iterating from 1 ` `    ``int` `i = 1; ` ` `  `// Infinite loop ` `    ``while` `(``true``) { ` ` `  `        ``// Finding ith_term ` `        ``int` `ith_term = (2 * i + 1)  ` `* (i * i + i + 1); ` ` `  `        ``// Checking if the number N ` `        ``// is a Centered cube number ` `        ``if` `(ith_term == N) { ` `            ``return` `true``; ` `        ``} ` ` `  `        ``// If ith_term > N then ` `        ``// N is not a Centered cube number ` `        ``if` `(ith_term > N) { ` `            ``return` `false``; ` `        ``} ` ` `  `        ``// Incrementing i ` `        ``i++; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N = 9; ` ` `  `    ``// Function call ` `    ``if` `(isCenteredcube(N)) { ` `        ``cout << ``"Yes"``; ` `    ``} ` `    ``else` `{ ` `        ``cout << ``"No"``; ` `    ``} ` `    ``return` `0; ` `} `

## Java

 `// Java program to check if N  ` `// is a centered cubic number  ` `class` `GFG{  ` ` `  `// Function to check if N  ` `// is a centered cubic number  ` `static` `boolean` `isCenteredcube(``int` `N)  ` `{  ` `     `  `    ``// Iterating from 1  ` `    ``int` `i = ``1``;  ` `     `  `    ``// Infinite loop  ` `    ``while` `(``true``) ` `    ``{  ` `         `  `        ``// Finding ith_term  ` `        ``int` `ith_term = (``2` `* i + ``1``) *  ` `                       ``(i * i + i + ``1``);  ` ` `  `        ``// Checking if the number N  ` `        ``// is a centered cube number  ` `        ``if` `(ith_term == N) ` `        ``{  ` `            ``return` `true``;  ` `        ``}  ` ` `  `        ``// If ith_term > N then N is   ` `        ``// not a centered cube number  ` `        ``if` `(ith_term > N)  ` `        ``{  ` `            ``return` `false``;  ` `        ``}  ` ` `  `        ``// Incrementing i  ` `        ``i++;  ` `    ``}  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``int` `N = ``9``;  ` ` `  `    ``// Function call  ` `    ``if` `(isCenteredcube(N)) ` `    ``{  ` `        ``System.out.println(``"Yes"``); ` `    ``} ` `    ``else` `    ``{ ` `        ``System.out.println(``"No"``); ` `    ``} ` `}  ` `}  ` ` `  `// This code is contributed by shubham `

## Python3

 `# Python3 program to check if N  ` `# is a centered cubic number  ` ` `  `# Function to check if N  ` `# is a centered cubic number  ` `def` `isCenteredcube(N): ` ` `  `    ``# Iterating from 1  ` `    ``i ``=` `1``;  ` `     `  `    ``# Infinite loop  ` `    ``while` `(``True``): ` `     `  `        ``# Finding ith_term  ` `        ``ith_term ``=` `((``2` `*` `i ``+` `1``) ``*` `                    ``(i ``*` `i ``+` `i ``+` `1``));  ` ` `  `        ``# Checking if the number N  ` `        ``# is a centered cube number  ` `        ``if` `(ith_term ``=``=` `N): ` `            ``return` `True``;  ` `         `  `        ``# If ith_term > N then N is  ` `        ``# not a centered cube number  ` `        ``if` `(ith_term > N): ` `            ``return` `False``;  ` `         `  `        ``# Incrementing i  ` `        ``i ``+``=` `1``;  ` `     `  `# Driver code  ` `N ``=` `9``;  ` ` `  `# Function call  ` `if` `(isCenteredcube(N)): ` `    ``print``(``"Yes"``); ` `else``: ` `    ``print``(``"No"``); ` ` `  `# This code is contributed by Code_Mech `

## C#

 `// C# program to check if N  ` `// is a centered cubic number  ` `using` `System; ` `class` `GFG{  ` ` `  `// Function to check if N  ` `// is a centered cubic number  ` `static` `Boolean isCenteredcube(``int` `N)  ` `{  ` `     `  `    ``// Iterating from 1  ` `    ``int` `i = 1;  ` `     `  `    ``// Infinite loop  ` `    ``while` `(``true``) ` `    ``{  ` `         `  `        ``// Finding ith_term  ` `        ``int` `ith_term = (2 * i + 1) *  ` `                       ``(i * i + i + 1);  ` ` `  `        ``// Checking if the number N  ` `        ``// is a centered cube number  ` `        ``if` `(ith_term == N) ` `        ``{  ` `            ``return` `true``;  ` `        ``}  ` ` `  `        ``// If ith_term > N then N is  ` `        ``// not a centered cube number  ` `        ``if` `(ith_term > N)  ` `        ``{  ` `            ``return` `false``;  ` `        ``}  ` ` `  `        ``// Incrementing i  ` `        ``i++;  ` `    ``}  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main() ` `{ ` `    ``int` `N = 9;  ` `     `  `    ``// Function call  ` `    ``if` `(isCenteredcube(N)) ` `    ``{  ` `        ``Console.WriteLine(``"Yes"``); ` `    ``} ` `    ``else` `    ``{ ` `        ``Console.WriteLine(``"No"``); ` `    ``} ` `}  ` `}  ` ` `  `// This code is contributed by shivanisinghss2110 `

Output:

```Yes
```

Time Complexity: O(N).

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